Greatest possible error

key notes :

Definition

• The Greatest Possible Error (GPE) is the maximum amount by which a measured value could differ from the true value due to limitations of the measuring instrument.
• It represents the uncertainty of a measurement.

How to Calculate GPE

• The GPE is half of the smallest measurement unit of the instrument used.
• Formula:

Greatest Possible Error = Smallest Division of the Instrument / 2

• Example: If a ruler measures in millimeters (mm), the GPE is 1/2 mm = 0.5 mm.

Why GPE Matters

• Helps understand the accuracy and precision of measurements.
• Essential in fields like science, engineering, and construction, where exact measurements are crucial.

Absolute Error vs. Relative Error

• Absolute Error: The GPE expressed in measurement units (e.g., ±0.5 cm).
• Relative Error: The GPE divided by the measured value, often expressed as a percentage.

Example Problem

If you measure a table’s length as 100 cm using a ruler with 1 cm divisions:

GPE = 1 cm / 2 = 0.5 cm

The actual length could be between 99.5 cm and 100.5 cm.

Importance in Real-Life Scenarios

• In construction, small errors can lead to significant structural problems.
• In scientific experiments, GPE helps determine the confidence level of results.

Key Terms to Remember

• Precision: How detailed a measurement is.
• Accuracy: How close a measurement is to the true value.
• Uncertainty: The range in which the true value is expected to lie.

Learn with an example

Let’s practice!🖊️